I separate my stuff into separate Gro-via drawstring wet bags (dipes, snacks, change of clothes, misc supplies) and then I can use whatever bag I feel like since I just move the inner bags. It's worked great for us.

For quick trips I usually just take my Planetwise wet/dry bag. It fits two (compact) changes, wipes, a (compact) change of clothes and a sippy cup (with cap). It even fits all that after it "lost a limb" in a near-catastrophic accident.

For longer trips we generally use a traditional diaper bag. If we're going somewhere nicer I put the wet/dry and 1-2 more changes and a snack trap in my large Michael Kors bag (a leather anniversary/new mommy gift from my awesome DH!).